Abstract

We examine the effects of encoder and decoder mismatch due to wavelength and time chip misalignments on the bit-error rate (BER) performance of two-dimensional (2D) wavelength–time optical code-division multiple access systems. We investigate several instances of misalignment in the desired user encoder and decoder as well as in the interfering user encoders. Our simulation methodology can be used to analyze any type of 2D wavelength–time code family as well as probability distribution for misalignment. For illustration purposes, we consider codes generated by use of the depth-first search algorithm and a Gaussian distribution for the misalignment. Our simulation results show that, in the case of a misalignment in either wavelength or time chip, the variance of the distribution for the misalignment must be below 0.01 for the corresponding degradation in the BER system’s performance to be less than 1 order of magnitude compared with that when there is no mismatch between the encoders and decoders. The tolerances become even more strict when misalignments in both wavelength and time chips are considered. Furthermore, our results show that the effect of misalignment in wavelength (time chips) is the same regardless of the number of wavelengths (time chips) used in the codes.

We note that good mechanisms exist to keep the wavelengths of optical filters locked. Moreover, the filter responses can be designed to have boxlike shapes with flat tops and high adjacent-channel cross-talk rejection. Thus, from a practical perspective, we expect wavelength misalignments to be typically a fraction of one wavelength band. Optical path differences (improperly defined delay lines), however, can cause time chip misalignments to extend beyond one time chip. The actual extent will depend on the precision in fabricating and controlling the optical delays as well as on the chip rate of the system. As the chip rate increases, the corresponding chip time decreases, such that a given optical path difference will result in time misalignments extending over a larger fraction of a time chip or even over multiple time chips. In our simulations we do not consider path differences that extend beyond a single time chip, though such situations are straightforward and easy to handle.

We note that good mechanisms exist to keep the wavelengths of optical filters locked. Moreover, the filter responses can be designed to have boxlike shapes with flat tops and high adjacent-channel cross-talk rejection. Thus, from a practical perspective, we expect wavelength misalignments to be typically a fraction of one wavelength band. Optical path differences (improperly defined delay lines), however, can cause time chip misalignments to extend beyond one time chip. The actual extent will depend on the precision in fabricating and controlling the optical delays as well as on the chip rate of the system. As the chip rate increases, the corresponding chip time decreases, such that a given optical path difference will result in time misalignments extending over a larger fraction of a time chip or even over multiple time chips. In our simulations we do not consider path differences that extend beyond a single time chip, though such situations are straightforward and easy to handle.

Figures (9)

Example of a code using m = 6 wavelengths, n = 6 time chips, and weight w = 6. (a) Ideal situation. The pulse at position (λ2, t4) suffers (b) a wavelength misalignment, (c) a time chip misalignment, and (d) both a wavelength and a time chip misalignment.